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In this paper, by rigorous calculations, we consider $L^2({\mathbb{R}})-spectrum$ of linear differential operators with periodic coefficients. These operators are usually seen in linearization of nonlinear partial differential equations about spatially periodic traveling wave solutions. Here, by using the solution operator obtained from Floquet theory, we prove rigorously that $L^2({\mathbb{R}})-spectrum$ of the linear operator is determined by the eigenvalues of Floquet matrix.
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참고문헌 (8)
참고문헌 신청
M. Johnson / 2011 / Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction diffusion equations / Ann. Inst. H. Poincare Anal. Non Lineaire 28(4):471~483
M. Johnson / 2013 / Nonlocalized Modulation of Periodic Reaction Diffusion Waves: Nonlinear Stability / Arch. Rational Mech. Anal 207:693~715
M. Johnson / 2014 / Behavior of periodic solu-tions of viscous conservation laws under localized and nonlocalized perturbations / Invent. Math 197(1):115~213
S. Jung / 2012 / Pointwise asymptotic behavior of modulated periodic reaction-diffusion waves / J. Differential Equations 253(6):1807~1861
S. Jung / 2014 / Pointwise stability estimates for periodic traveling wave solutions of systems of viscous conservation laws / J. Differential Equations 256(7):2261~2306
M. Johnson / 2013 / Nonlocalized Modulation of Periodic Reaction Diffusion Waves: Nonlinear Stability / Arch. Rational Mech. Anal 207:693~715
M. Johnson / 2014 / Behavior of periodic solu-tions of viscous conservation laws under localized and nonlocalized perturbations / Invent. Math 197(1):115~213
S. Jung / 2012 / Pointwise asymptotic behavior of modulated periodic reaction-diffusion waves / J. Differential Equations 253(6):1807~1861
S. Jung / 2014 / Pointwise stability estimates for periodic traveling wave solutions of systems of viscous conservation laws / J. Differential Equations 256(7):2261~2306
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